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Math Help - Continuous Function

  1. #1
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    Continuous Function

    for which value of the constant K is the function h(x)=\left\{\begin{array}{cc}\frac{e^x -e^a}{x-a},&\mbox{ if }<br />
x\ne a\\K, & \mbox{ if } x=a\end{array}\right.

    continuous at x=a. justify your answer.

    Answer
    \lim_{x \rightarrow a} h(x) = \lim_{x \rightarrow a} \frac{e^x - e^a}{x-a}

    h(a) = K and the other limit is e^a \log(e)

    so is K = e^a \log(e)?, is this a correct way of answering the question
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  2. #2
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    Quote Originally Posted by iLikeMaths View Post
    for which value of the constant K is the function h(x)=\left\{\begin{array}{cc}\frac{e^x -e^a}{x-a},&\mbox{ if }<br />
x\ne a\\K, & \mbox{ if } x=a\end{array}\right.

    continuous at x=a. justify your answer.

    Answer
    \lim_{x \rightarrow a} h(x) = \lim_{x \rightarrow a} \frac{e^x - e^a}{x-a}

    h(a) = K and the other limit is e^a \log(e)

    so is K = e^a \log(e)?, is this a correct way of answering the question
    yes, but log should be natural log, and also \ln(e)=1.
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  3. #3
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    so K =e^a thanks
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